simple cross – over design ( แผนการทดลองแบบเปลี่ยน...

Simple Cross Simple Cross –– over Design over Design((แผนการทดลองแบบเปล��ยนสล�บแผนการทดลองแบบเปล��ยนสล�บ

อย�างง�ายอย�างง�าย))

ByByDr.Wuttigrai BoonkumDr.Wuttigrai Boonkum

Dept.Animal Science, Fac. AgricultureDept.Animal Science, Fac. AgricultureKKUKKU

Simple Cross-Over DesignSimple Cross-Over Design

• Other name “Simple Change-over Other name “Simple Change-over Design” or “Reversal design”Design” or “Reversal design”

• Look like Repeated Measurement Exp.Look like Repeated Measurement Exp.• About 3 factors are treatments, Animal About 3 factors are treatments, Animal

and time.and time.• Researcher must change – over all Researcher must change – over all

treatments in each animal.treatments in each animal.• Response measured of treatment effect Response measured of treatment effect

in each animal and each timein each animal and each time..

ObjectiveObjective

• To compare between cross-over design To compare between cross-over design and switch-back design.and switch-back design.

• Can calculated statistic parameters in Can calculated statistic parameters in cross-over design and switch-back cross-over design and switch-back design.design.

• Can interpretation and conclusion of Can interpretation and conclusion of results from SAS program.results from SAS program.

• Tell differentiate of Type of Replicated Tell differentiate of Type of Replicated Latin Square.Latin Square.

Step by Step of Cross-over Step by Step of Cross-over Design Design

Classify FactorsClassify Factors

Consideration of number of Animal, Treatment and Time Consideration of number of Animal, Treatment and Time

Statistical model, Hypothesis setting, Lay outStatistical model, Hypothesis setting, Lay out

ANOVA analysis using SAS programANOVA analysis using SAS program

Interpretation and ConclusionInterpretation and Conclusion

Statistical modelStatistical model

ijkkjiijky

error

effecttreatment

effectcolumn

effectrow

meanoverall

treatmentofnobservatioy

ijk

k

j

i

ijk

Hypothesis settingHypothesis setting

• Look like Latin Square Design such as:Look like Latin Square Design such as:• Trt = 2, hypothesis is:Trt = 2, hypothesis is:

21

210

:

:

AH

H

Lay outLay out

A A B A B B

B B A B A A

Period1Period1

Period2Period2

A A B A B -

B B A B A A

Period1Period1

Period2Period2

Transition period

Resting period

12 EU.; A = Animal

A1 A2 A3 A4 A5 A6

SAS codeSAS code

Data……;Data……; input row col trt y;input row col trt y;Cards;Cards; x x x xx x x x x x x xx x x x x x x xx x x x;;Proc anova data =………….;Proc anova data =………….; class row col trt;class row col trt; model y = row col trt;model y = row col trt; means trt /duncan;means trt /duncan;Run;Run;

Like Latin square design

SAS outputSAS output

ANOVAANOVA TableTable

SOV df SS MS F P-value

Period p-1

Animal a-1

Treatment

t-1

Error (t-1)*(t-2)

Total n-1

Interpretation is likely LSD

P-value > 0.05 non-significant; nsP-value < 0.05 significant; *P-value < 0.01 highly significant; **

AdvantagesAdvantages

1. Have efficiency more than CRD

2. Good for budget limitation

3. Increase precision for Experimental design

Switch-back DesignSwitch-back Design

• Look like cross-over design. Look like cross-over design.

• But turn around 1But turn around 1stst treatment when treatment when cross-over each treatments.cross-over each treatments.

• This design is appropriate for high This design is appropriate for high effect of time on treatmenteffect of time on treatment

• The example this design such as: The example this design such as: lactation trait, growth trait, traits about lactation trait, growth trait, traits about time period etc.time period etc.

ExampleExampleA

A

B

B

B

ASequence A B A

Sequence B A B

Lay outLay out

AA AA BB AA BB BB

BB BB AA BB AA AA

AA AA BB AA BB BB

Period1Period1

Period2Period2

Period3Period3

Sequence A B A

This lay out have 2 sequence:

Sequence B A B

Animal 1 Animal 2 Animal 3 Animal 4 Animal 5 Animal 6

18 EU.


ijkijjikiijky )(

error

errorsequencewithinanimal

effectperiodandeffectsequenceoferactionint

effectperiod

effectsequence

meanoverall

treatmentofnobservatioy

ijk

ik

ij

j

i

ijk

)(

Hypothesis settingHypothesis setting• Look like Cross-over Design such as:Look like Cross-over Design such as:• Trt = 2, hypothesis is:Trt = 2, hypothesis is:

0)(2:

0)(2:

02/)(:

02/)(:

0

0

BAH

BAH

or

BAAH

BAAH

A

A

0)(2:

0)(2:

02/)(:

02/)(:

0

0

ABH

ABH

or

ABBH

ABBH

A

A

Sequence B A B Sequence A B A

ANOVAANOVA

Note: Animal(sq) = Animal within sequence error; P = Period (is regression)

SOV df SS MS F P-value

Sequence s-1

Animal(sq) s(a-1)

Period p-1

P*Sequence 1*(s-1)

P*Animal(sq) 1*s(a-1)

Treatment t-1

Error dftot-dfother

Total n-1

SAS codeSAS codeData……;Data……; input row col trt observ;input row col trt observ; If cow = 1 or cow = 2 or cow = 3 THEN seq = 1 ELSE seq = 2;If cow = 1 or cow = 2 or cow = 3 THEN seq = 1 ELSE seq = 2;P = period;P = period;Cards;Cards; x x x xx x x x x x x xx x x x x x x xx x x x;;Proc GLM data =………….;Proc GLM data =………….; class seq cow period trt ;class seq cow period trt ; model observ = seq cow(seq) period p*seq p*cow(seq) trt /SS1;model observ = seq cow(seq) period p*seq p*cow(seq) trt /SS1; Test H = period p*seq E = p*cow(seq);Test H = period p*seq E = p*cow(seq); Test H = seq E = cow(seq);Test H = seq E = cow(seq); Lsmeans trt ;Lsmeans trt ;Run;Run;

SAS outputSAS output

InterpretationInterpretation

Check P-value of adjusted p * sequence interaction

Check P-value of adjusted period and sequence respectively

Check P-value of treatment effect

ns * , **

conclusion Treatment mean analysis

AdvantagesAdvantages

• Precision morn than cross-over design

• Appropriate for time period traits

Replicated Latin Square DesignReplicated Latin Square Design

• Use case more than 2 treatmentUse case more than 2 treatment

• Researcher want to change-over trt.Researcher want to change-over trt.

• To decrease error of sequence so must To decrease error of sequence so must have a square.have a square.

• Each square must difference of Each square must difference of sequence so may be called “balanced sequence so may be called “balanced square” or “orthogonal square”.square” or “orthogonal square”.

Replicated Latin Square DesignReplicated Latin Square Design

3 type of Replicated Latin Square3 type of Replicated Latin Square

1. Type I: originally animal set, time difference.1. Type I: originally animal set, time difference.

Square1 Square2

Period Anim 1 Anim 2 Anim 3 Period Anim 1 Anim 2 Anim 3

1 C B A 4 A C B

2 A C B 5 C B A

3 B A C 6 B A C

2. Type II: new animal set, same time.2. Type II: new animal set, same time.

Square1 Square2


1 C B A 1 A C B

2 A C B 2 C B A

3 B A C 3 B A C

3. Type III: new animal set, time difference.3. Type III: new animal set, time difference.

Square1 Square2


1 C B A 4 A C B

2 A C B 5 C B A

3 B A C 6 B A C

Orthogonal or balanced squareOrthogonal or balanced square

Example : A, B, C and D are treatmentsExample : A, B, C and D are treatments

CCBBAA

AA

AA

AA

DD

CCBB DD

CCBBDD

CC BBDD

Orthogonal or balanced squareOrthogonal or balanced square

Example : A, B, C, D and E are treatmentsExample : A, B, C, D and E are treatments

AA

AA

AA

AA

AA

Statistical model and ANOVAStatistical model and ANOVA

SOVSOV DfDf

SqSq s-1s-1

AnimAnim p-1p-1

P(Sq)P(Sq) s(p-1)s(p-1)

TT p-1p-1

ErrorError spsp22-p(s+2)+2-p(s+2)+2

TotalTotal spsp22-1-1

ijklkljilijkl TPASyAType )(:


SOVSOV DfDf

SqSq s-1s-1

Anim(Sq)Anim(Sq) s(p-1)s(p-1)

PP p-1p-1

TT p-1p-1

ErrorError spsp22-p(s+2)+2-p(s+2)+2


ijklkjlilijkl TPASyBType )(:


SOVSOV DfDf

SqSq s-1s-1

Anim(Sq)Anim(Sq) s(p-1)s(p-1)

P(Sq)P(Sq) s(p-1)s(p-1)

TT p-1p-1

ErrorError spsp22-p(2s+1)+s+1-p(2s+1)+s+1


ijklkljlilijkl TPASyCType )()(:

SAS codeSAS code• Type A:Type A:

Proc anova data = ……….;Proc anova data = ……….;

class sq anim period trt;class sq anim period trt;

model Y = sq anim model Y = sq anim period(sq)period(sq) trt; trt;

means trt /Duncan;means trt /Duncan;

Run;Run;

• Type B:Type B:



model Y = sq model Y = sq anim(sq)anim(sq) period trt; period trt;

means trt /Duncan;means trt /Duncan;

Run;Run;

SAS codeSAS code• Type C:Type C:



model Y = sq model Y = sq anim(sq) period(sq)anim(sq) period(sq) trt; trt;

means trt /BON;means trt /BON;

Run;Run;

SAS outputSAS output Type AType A

SAS outputSAS output Type BType B

SAS outputSAS output Type CType C

Latin square Design to Estimate Latin square Design to Estimate Residual EffectsResidual Effects

• Transition period limited.Transition period limited.

• Some treatments may have residual Some treatments may have residual effects.effects.

• Sometime Researcher interested in Sometime Researcher interested in residual effects.residual effects.

• Example residual effects such as Example residual effects such as antibiotic, hormones etc. antibiotic, hormones etc.

SAS data setSAS data setData;Data; input sq anim period trt $ milk Resid;input sq anim period trt $ milk Resid;Cards;Cards;1 1 1 A 38 1 1 1 A 38 XX1 1 2 B 25 A1 1 2 B 25 A1 1 3 C 15 B1 1 3 C 15 B1 2 1 B 109 1 2 1 B 109 X X1 2 2 C 86 B1 2 2 C 86 B1 2 3 A 39 C1 2 3 A 39 C1 3 1 C 124 1 3 1 C 124 XX1 3 2 A 72 C1 3 2 A 72 C1 3 3 B 27 A1 3 3 B 27 A2 4 4 A 86 2 4 4 A 86 XX2 4 5 C 76 A2 4 5 C 76 A2 4 6 B 46 C2 4 6 B 46 C2 5 4 B 75 2 5 4 B 75 XX2 5 5 A 35 B2 5 5 A 35 B2 5 6 C 34 A2 5 6 C 34 A2 6 4 C 101 2 6 4 C 101 XX2 6 5 B 63 C2 6 5 B 63 C2 6 6 A 1 B2 6 6 A 1 B;;

XX

AA

BB

SAS codeSAS code

Proc GLM data =……….;Proc GLM data =……….;

class sq anim period trt resid;class sq anim period trt resid;

model model milk = sq anim(sq) period(sq) trt resid;milk = sq anim(sq) period(sq) trt resid;

Run;Run;

Graeco Latin Square DesignGraeco Latin Square Design

• Researcher can separate a variable Researcher can separate a variable later (greek letter) later (greek letter)

• Level of effects equal row effect, Level of effects equal row effect, column effect and treatment effect.column effect and treatment effect.


effecttreatment

effectgreek

effectcolumn

effectrow

meanoverall

nobservatioy

when

y

l

k

j

i

ijkl

ijkllkjiijkl

Lay outLay outrow Col 1 Col 2 Col 3 row Col 1 Col 2 Col 3

1 A B C 1 α β γ

2 B C A 2 γ α β

3 C A B 3 β γ α

row Col 1 Col 2 Col 3

1A

αB

βC

γ

2B

γC

αA

β

3C

βA

γB

α

SAS codeSAS codeData…………; input row col trt $ greek $ observe;Cards;x x x x xx x x x xx x x x xx x x x x;Proc anova data =…..; class row col greek trt; model observe = row col greek trt; means trt / duncan;Run;

ANOVAANOVA of Graeco Latin Square of Graeco Latin Square DesignDesign

SOVSOV DfDf

RowRow r-1r-1

ColumnColumn c-1c-1

TreatmentTreatment t-1t-1

GreekGreek g-1g-1

ErrorError ResidualsResiduals

TotalTotal n-1n-1

The EndThe EndNext time I will lecture about …Next time I will lecture about …

Incomplete block designIncomplete block design

simple cross – over design ( แผนการทดลองแบบเปลี่ยน...

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